Space of modular forms of level 100, weight 2, and Character 100.e

• Label: 100.2.e
• Level: $100$
• Weight: $2$
• Character orbit: 100.e
• Rep. character: $\chi_{100}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $14$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(30\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).

	Total	New	Old
Modular forms	42	22	20
Cusp forms	18	14	4
Eisenstein series	24	8	16

Trace form

14 * q + 2 * q^2 - 12 * q^6 - 4 * q^8 + 2 * q^13 + 4 * q^16 - 6 * q^17 + 6 * q^18 - 24 * q^21 - 20 * q^26 - 8 * q^32 + 12 * q^36 + 14 * q^37 + 8 * q^41 + 48 * q^46 + 4 * q^52 - 18 * q^53 + 48 * q^56 - 8 * q^58 - 72 * q^61 + 60 * q^66 + 12 * q^68 + 12 * q^72 + 22 * q^73 - 60 * q^76 + 90 * q^81 - 16 * q^82 - 72 * q^86 - 132 * q^96 - 26 * q^97 - 14 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.2.e.a	$100$	$2$	100.e	20.e	$4$	$2$	$1$	$0.799$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)		✓			100.2.e.a	$4$	$0$	\(-2\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i-1)q^{2}+(-i-1)q^{3}-2 i q^{4}+\cdots\)
100.2.e.b	$100$	$2$	100.e	20.e	$4$	$2$	$1$	$0.799$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					20.2.e.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i+1)q^{2}+2 i q^{4}+(2 i-2)q^{8}+\cdots\)
100.2.e.c	$100$	$2$	100.e	20.e	$4$	$2$	$1$	$0.799$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)		✓			100.2.e.a	$4$	$0$	\(2\)	\(2\)	\(0\)	\(-6\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i+1)q^{2}+(i+1)q^{3}-2 i q^{4}+\cdots\)
100.2.e.d	$100$	$2$	100.e	20.e	$4$	$8$	$4$	$0.799$	8.0.3317760000.5	None		✓	✓		100.2.e.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)